European Journal of Soil Science, August 2007, 58, 932–944
doi: 10.1111/j.1365-2389.2007.00931.x
Surface complex structures modelled with quantum
chemical calculations: carbonate, phosphate,
sulphate, arsenate and arsenite
J. D. K UBICKI a , K. D. K WON a , K. W. P AUL b & D. L. S PARKS b
a
The Pennsylvania State University, Department of Geosciences and the Earth and Environmental Systems Institute, University Park,
PA 16802, and bUniversity of Delaware, Department of Plant and Soil Sciences, Newark, DE 1971,7 USA
Summary
Hybrid molecular orbital/density functional theory (MO/DFT) calculations on molecular clusters were
used to model infrared (IR) vibrational frequencies and interatomic distances obtained via extended X-ray
absorption fine structure (EXAFS) spectroscopy. Molecular clusters were found to provide good agreement with experimental observations for the oxyanions carbonate, phosphate, sulphate, arsenate and
arsenite. The results show a consistent tendency to form bidentate bridging surface complexes at low
pH, but the protonation and hydration states play a significant role in the results obtained from calculation
as various protonation states of monodentate surface complexes are also predicted to be stable as pH
increases (i.e. the number of Hþ ions in the model are decreased). A method for estimating the Gibbs
free energy of adsorption (DGads) is discussed to complement the comparisons of experimental and theoretical spectroscopic parameters. Calculated DGads values were consistent with the interpretations
based on modelling observed spectra.
Introduction
Sorption of oxyanions is a common and important process in
soils. Whether affecting the availability of nutrients or the transport of contaminants, the interaction of species such as carbonate, phosphate, sulphate, arsenate and arsenite with metal oxide
and clay surfaces must be understood to predict their transport
behaviour. Oxyanion surface complexes have been studied using
a variety of techniques, such as Fourier transform infrared
(FTIR) and EXAFS spectroscopy in order to help constrain
surface complexation models. However, interpretation of the
spectroscopic data is not always unambiguous. In these cases,
molecular modelling can help make spectral assignments and
provide valuable input to surface complexation modelling studies (Zhang et al., 2004; Fitts et al., 2005). This paper will examine principles behind modelling the oxyanion surface
complexes and provide examples of how these principles can
be applied to soil chemical and geochemical problems.
To begin understanding oxyanion adsorption to mineral surfaces, molecular modelling of carbonate, phosphate, sulphate,
arsenate and arsenite interactions with Al and Fe hydroxide
dimers was performed (Kwon & Kubicki, 2004; Bargar et al.,
Correspondence: J. Kubicki. E-mail: kubicki@geosc.psu.edu
Received 24 February 2007; revised version accepted 14 May 2007
932
2005; Paul et al., 2005; Kubicki, 2005). This suite of oxyanions
is not comprehensive nor is the selection of model substrates
meant to simulate every adsorption reaction for these compounds in the environment. However, amorphous and crystalline Al and Fe (hydr)oxides are important reactive minerals in
many soils throughout the world and metal oxides have been
established as some of the most important substrates in environmental chemistry (Brown et al., 1999). These models were
used to demonstrate how important molecular scale information can be obtained using computational chemistry and to
explore how environmental factors (e.g. including solvation by
H2O) affect the accuracy of results. By obtaining results for
each compound with similar methodologies, individual systems may be comparable (e.g. predictions for surface complex
structures and adsorption energies).
Carbonate is a ubiquitous anion in soils and groundwaters.
Carbonate complexation to metals in soil solution and on mineral
surfaces is appreciable; hence understanding the surface speciation of carbonate is a prerequisite to investigating other oxyanion
adsorption behaviour. Generally, carbonate will compete with
other soil solution species for surface sites (Appelo et al., 2002;
Wijnja & Schulthess, 2002; Arai et al., 2004). Modelling of
carbonate adsorption onto haematite (a-Fe2O3) was performed
to assess the utility of applying computational chemistry
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Journal compilation # 2007 British Society of Soil Science
Surface complexes and quantum chemical calculations 933
calculations on molecular clusters as models of surface reactions (Bargar et al., 2005). In addition, the role of coadsorbed
H2O on predicted vibrational frequencies was investigated.
Phosphorus is an essential plant and animal nutrient and
a component of biopolymers found in soils (Omoike et al.,
2004). Unmanaged P (typically as phosphate) losses from
watersheds are known to degrade water quality, for example
in eutrophication. The transport and bioavailability of phosphate in soils is partly regulated by sorption reactions with Al
and Fe (hydr)oxides. Phosphate sorption should be understood at the molecular scale in order to manage it effectively in
the environment. Quantum chemical calculations were performed to help resolve controversy regarding phosphate surface complexes on Fe (hydr)oxides from IR studies (Kwon &
Kubicki, 2004). Molecular modelling of six possible surface
complexes was conducted to assess potential surface complexes. The calculated IR frequencies were compared to experimental IR frequency data (Persson et al., 1996; Arai &
Sparks, 2001). In addition, reaction energies of phosphate
adsorption were calculated.
Sulphur is also an essential plant and animal nutrient (sulphate is the most common form absorbed). Sulphate may
become highly concentrated in soils due to geochemical cycling
of metal sulphides (particularly pyrite) or to field-scale application of alum (Al2(SO4)3) which is used to sequester phosphate
in soil management practice. Recently, attenuated total reflectance (ATR) FTIR complemented by quantum chemical calculations was used to investigate sulphate adsorption on Fe
(hydr)oxides and oxidized pyrite (Paul et al., 2005; Usher et al.,
2005). Details of the coordination geometry and species were
acquired by determining which model surface complexes best
correlated with measured ATR FTIR frequencies. In this
manner, the number of Fe-O-S bonds and the protonation
state of sulphate were assessed.
Arsenic contamination of soil and water resources around the
world has gained significant attention. Sorption of As to Al and
Fe (hydr)oxides is important in the transport of As in soils and
aquifers and in wastewater treatment processes. Recent studies
have observed strong adsorption of As(V) onto Al and Fe
(hydr)oxides (Dixit & Hering, 2003). However, As(III) was
observed to adsorb less to Al (hydr)oxides than to Fe (hydr)oxides. Quantum chemical calculations were performed for
previously proposed surface complexes of As(III) and As(V)
on Al and Fe (hydr)oxides. Comparison of calculated and measured vibrational frequencies for aqueous As species suggests
that the molecular modelling approaches may be able to describe
As bonding adequately. Interatomic distances of model surface
complexes were compared to values derived from EXAFS studies (Waychunas et al., 1993; Fendorf et al., 1997; Manning
et al., 1998; Arai et al., 2001; Farquhar et al., 2002; Sherman &
Randall, 2003).
Computational chemistry and molecular modelling tools are
capable of addressing complex soil chemistry research questions
and advancing our understanding of nutrient management and
contaminant behaviour in soils. This paper highlights some of
the recent successful investigations in which computational
chemistry has complemented experimental research, and ultimately afforded detailed insight into important soil chemistry
issues. As the ability to model soil chemical reactions of greater
complexity improves, experimentalists and modellers will be
able to integrate their respective approaches more fully.
Methods
Calculations were performed using the Gaussian 03 program
(Frisch et al., 2003). Models were built with the Cerius2 suite
of programs (Accelrys Inc., San Diego, CA, USA). Visualization of vibrational modes was performed with the Molden
program (Schaftenaar & Noordik, 2000). Most computations
were performed on Linux clusters run by the Graduate Education and Research Services (GEaRS) at The Pennsylvania
State University (PSU) in conjunction with the Materials Simulation Center (www.msc.psu.edu) of the PSU Materials
Research Institute and the Center for Environmental Kinetics
Analysis (www.ceka.psu.edu). Model calculations of this size
typically run efficiently on 8–16 processors and require less
than 100 hours of CPU time; 512 MB of RAM/processor is
generally sufficient to perform calculations of the size and
basis set discussed in this paper.
Calculations were performed with a hybrid MO/DFT
method. MO/DFT is a computationally efficient method for
estimating electron correlation effects. The 3-parameter electron
exchange functional of Becke (1993) was used in combination
with the electron exchange energy derived from Hartree-Fock
theory (Foresman & Frisch, 1996). The correlation functional of
Lee et al. (1988) was used to account for electron correlation.
The basis sets 6–31G(d), 6–31þG(d), and 6–311 þ G(d,p)
(Krishnan et al., 1980; McLean & Chandler, 1980; Petersson
et al., 1988) were employed for energy minimizations, frequency calculations, and single-point energy calculations on
various cluster models. The particular basis set associated with
each result will be noted.
Cluster models were energy-minimized with internal redundant coordinates (Peng et al., 1996) and without symmetry or
geometrical constraints. The use of internal redundant coordinates speeds up the process of finding potential energy minima for molecules because the derivatives of the potential
energy with respect to all atomic interactions are calculated at
each step. Typically, there are 3N–6 internal coordinates
(where N is the number of atoms in a molecule and the 6 subtracts the rotations and translations of the molecule) required
to describe atomic positions. However, using internal redundant coordinates allows the atomic positions to be adjusted
into new lower energy positions more accurately than the minimum 3N–6 derivatives because all atomic interactions are
accounted for simultaneously.
Default energy and structure convergence criteria in Gaussian
03 (Frisch et al., 2003) were used. All nuclear positions in the
# 2007 The Authors
Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
934 J. D. Kubicki et al.
models were allowed to relax to minimum potential energy
positions, which is required before performing frequency calculations (i.e. the potential energy derivative for all atomic displacements must be equal to 0 in order for the harmonic
approximation to be applicable). An analytical method to
solve the second derivative potential energy matrix (i.e. the
Hessian matrix) provided the model frequencies. Calculated
frequency values were scaled by factors determined a priori to
account for anharmonicity, basis set limitations, and the inexact determination of electron correlation (Scott & Radom,
1996; Wong, 1996). Scaling factors reduced the calculated frequencies by approximately 4%.
Correlations of observed and calculated frequencies were
made by matching frequencies of vibrational modes with significant IR activity to measured frequencies. The algorithm of
Yamaguchi et al. (1986) for calculating infrared intensities (A)
analytically was used to obtain IR activities in km mol1
A ¼ ½1=ð100 C lÞ
ð
lnðIo =IÞ dn;
ð1Þ
where A is the activity (km mol1), C is the concentration (mol
litre1), l is the path length (cm), Io is the incident intensity,
and I is the intensity of the transmitted radiation and n is in
cm1 (see Overend, 1982; Kubicki et al., 1993). Although the
values of the IR intensities were not quantitatively used in the
current research, calculated IR intensities were used to identify
important IR-active frequencies to compare with observed
peaks. Vibrational mode assignments were made by visual
inspection of the atomic displacements created during the frequency calculation (i.e. the eigenvectors of the Hessian matrix)
using Molden (version 4.0; Schaftenaar & Noordik, 2000).
The effect of solvation on the energies of aqueous and surface
species was modelled by inclusion of explicit H2O molecules
near to each solute and adsorbate, including the initial surface
functional groups. Aqueous-phase Gibbs free energies were
based on the integral equation formalism polarized continuum
model (IEFPCM; Cancès et al., 1997; Cossi et al., 2002), which
accounts for iondipole and dipoledipole interactions not
obtained with explicit solvation of H2O molecules. This
‘supermolecule’ approach, where species are surrounded by
a shell of H2O and a dielectric continuum, has been shown to
be an effective method for modelling the effects of water on
calculated reaction energies (Keith & Frisch, 1994). A larger
basis set, 6–311þG(d,p), was used for these IEFPCM calculations. The thermal correction to the Gibbs free energy from
the gas-phase calculations with the B3LYP/6–31G(d) method
was added to the calculated aqueous Gibbs free energy.
Molecular cluster models were used (as opposed to 3-D periodic models) because they have proven to be an efficient method
for calculating vibrational frequencies and interatomic distances
for surface complexes. The specific models created are attempts
at balancing realism and practical computational matters. For
example, metal hydroxides, oxy(hydr)oxides and oxides often
hydrolyze when exposed to water, so our models include either
OH or OH2 as terminal groups around the Al3þ and Fe3þ cations. Many interpretations of adsorption data suggest that
bidentate bridging complexes are common for oxyanions;
hence we included two metal-oxide octahedra as the basis of
our surface. These octahedra are linked by OH groups because
similar structures may exist on surfaces of minerals such as
goethite (a-FeOOH) and diaspore (a-AlOOH). Although limited in their representation of some oxides, such as haematite
(a-Fe2O3), this model was chosen as a compromise between
the metal hydroxides and oxides. Good reproduction of
observed vibrational frequencies for surface complexes on
a variety of Al and Fe minerals has justified this simplification,
but more specific models can be created to mimic particular
mineral surfaces (Kubicki & Apitz, 1998).
One weakness of the molecular cluster model for surfaces is
that crystal structure constraints are not imposed upon the surface functional groups and surface complexes. Periodic models
may more realistically represent surfaces, but the calculated
vibrational frequencies and interatomic distances (as compared
with IR/Raman and EXAFS) have not yet proven to be superior
compared with molecular cluster models (research into this topic
is currently underway, see Paul et al., 2007, in this issue). Furthermore, current work on calculated Gibbs free energies of
adsorption suggests that the molecular cluster approach can
predict thermodynamics reasonably accurately. Hence, 3-D
periodic models have utility for examining longer-range effects
and defect structures; but, for our purposes here, the significant increase in computational time required is not justified.
Results
Carbonate adsorption on haematite
Haematite is common in soils and aquifers and is a strong adsorbent of oxyanions due to its positive surface charge at circumneutral pH. Although other Fe oxy(hydr)oxides are more
common in soils, similar adsorption mechanisms may be operative on these surfaces when examining inner-sphere complexation. Hence, haematite has been used as a model substrate
for examining adsorption of oxyanions to Fe oxy(hydr)oxide
surfaces.
At least 10 possible configurations exist for CO32– adsorption
onto Fe oxy(hydr)oxides (Bargar et al., 2005). Combinations
among the configurations of monodentate versus bidentate,
carbonate versus bicarbonate and inner- versus outer-sphere
adsorption contributed to the ambiguity of interpreting earlier
IR spectra (e.g. Su & Suarez, 1997; Wijnja & Schulthess,
2001). Moreover, the possibility that speciation could change
with pH and that several surface complexes could coexist
under any given set of conditions further complicated the situation. Consequently, Bargar et al. (2005) measured ATR
FTIR spectra of carbonate adsorbed onto haematite as a function of pH and with replacement of H2O by D2O. Systematic
# 2007 The Authors
Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
Surface complexes and quantum chemical calculations 935
data analysis of the spectra demonstrated a potential innersphere complex with C-Os and C-Oas modes (symmetric (s)
and asymmetric (as) C-O bond stretching which are the most
intense IR modes of carbonate vibrations) at 1320 and 1530
cm1, respectively. In addition, a potential outer-sphere complex with C-Os and C-Oas vibrations at 1360 and 1470 cm1,
respectively, was also observed.
MO/DFT calculations (B3LYP/6–31G(d)) were performed on
several variations of carbonate and bicarbonate adsorption, but
none of the model calculations provided predicted frequencies
within computational error (typically 20 cm1) of experimental
frequencies. The bidentate bridging configuration (Figure 1),
considered the most likely surface complex, resulted in frequencies in error by c. 200 cm1 with splitting between the C-Os and
C-Oas modes (Dm) of 542 cm1 (compared to the observed Dm of
210 cm1; Bargar et al., 2005). Bidentate bridging HCO3 predicted a Dm of 200 cm1; however, values of the C-Os and C-Oas
frequencies were in error by c. 100 cm1.
Previous results had shown much better agreement with
observed frequencies (Kubicki et al., 1997). Bargar et al. (2005)
hypothesized that the discrepancy may be due to the models
selected rather than the computational methodology. Earlier
papers on similar systems had shown that drying samples with
adsorbed oxyanions could significantly change the observed frequencies of the oxyanion surface complex (e.g. Hug, 1997;
Myneni et al., 1998). Because the samples in Bargar et al. (2005)
were not dried, two H2O molecules were added to form hydrogen bonds with the carbonate surface complexes (Figure 1b),
to mimic the in situ hydrated experiment. The effects were
dramatic. The aforementioned bidentate bridging carbonate frequencies (C-Os and C-Oas) changed from 1166 and 1708 cm1 to
1329 and 1524 cm1, respectively, within computational error of
the observed 1320 and 1530 cm1 bands. The calculated Dm
value decreased from 542 to 195 cm1, much closer to the
observed splitting of 210 cm1. Addition of four more H2O molecules changed the calculated frequencies by 10 cm1 or less,
indicating that inclusion of H-bonding was a key to obtaining
accurate model frequencies. Furthermore, this indicates that at
least a monolayer of water exists on mineral surfaces with adsorbed oxyanions even after air drying, due to strong H-bonding.
Solvating an outer-sphere carbonate anion near the Fe
(hydr)oxide cluster with 10 H2O molecules also resulted in
good agreement between observed (1360 and 1470 cm1) and
model C-Os and C-Oas frequencies (1346 and 1460 cm1).
Bargar et al. (2005) concluded that relatively simple molecular
cluster models were capable of predicting the vibrational
modes of mineral surface complexes. Furthermore, a moderate
level of theory was able to provide accurate results within
10–20 cm1 of the C-Os and C-Oas frequencies and Dm.
Phosphate adsorption on goethite
Based on the work of Persson et al. (1996) and Arai & Sparks
(2001), six possible species of orthophosphate (Figure 2) were
Figure 1 Carbonate on Fe2(OH)4(OH2)4 (a) without solvation and
(b) with solvation by two H2O molecules. H ¼ white, C ¼ black, O ¼
dark grey, and Fe ¼ light grey. Graphics created with Cerius2 (Accelrys Inc., San Diego, CA, USA).
thought to form on the surface of goethite (a-FeOOH) and
2-line ferrihydrite, respectively. These results highlight the
point that similar surface complexes of a given oxyanion can
form on a variety of mineral surfaces. IR interpretations
depended on the use of symmetry arguments to predict the
number of bands observed for surface phosphate complexes.
Hence, it was difficult to distinguish among species that varied
in the number of P-O-H and P-O-Fe bonds. As in the case of
carbonate adsorption, protonation states could also change as
a function of pH (Persson et al., 1996). Quantum chemical
calculations (B3LYP/6–31G(d)) were performed on the six
possible species to determine which model complex produced
# 2007 The Authors
Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
936 J. D. Kubicki et al.
Figure 2 Possible phosphate species for
adsorption onto Fe oxy(hydr)oxides. MD,
monodentate; BD, bidentate; H0, H1 and
H2, number of Hþ bonded to the phosphate.
H ¼ white, P ¼ black, O ¼ dark grey, and
Fe ¼ light grey. Graphics created with Cerius2
(Accelrys Inc.).
vibrational frequencies in best agreement with observation
(Kwon & Kubicki, 2004).
Phosphate surface complexes on goethite have four to six
observed IR modes. Deconvolution of these spectra to obtain
vibrational frequencies allows direct correlations to be made
between the experimental and calculated values. Correlation
of multiple peaks makes it possible to assign surface complexes
to observed spectra reliably and with better resolution among
similar structures. Figure 3 shows the calculated versus experimental correlations for acidic, neutral and basic pH conditions.
Under acidic and basic conditions, the diprotonated bidentate
(BD-H2) and unprotonated monodentate (MD-H0) surface
complexes, respectively, preferably formed. The BD-H2 correlation had a slope ¼ 1.00, R2 ¼ 0.99, and RMS error ¼ 15
cm1, significantly closer to the ideal values of 1, 1, and
0 cm1 than the other models (Kwon & Kubicki, 2004).
For spectra collected at pH 7.5 (Arai & Sparks, 2001) and 7.9
(Persson et al., 1996), the distinction between surface complexes was not as obvious. Two surface complexes, the deprotonated bidentate (BD-H0) and the monoprotonated
monodentate (MD-H1), resulted in accurate correlations with
the spectra presented in Arai & Sparks (2001) and Persson
et al. (1996), respectively. The measured spectra were different
because the experimental techniques and synthetic minerals
were not identical; hence it was impossible to assign one model
that accurately reproduced both data sets.
Estimates of the adsorption energy of each complex were calculated to help resolve this issue. Assuming a ligand exchange
reaction involving surface water,
Surface þ Aqueous species/Surface complex
þ Released H2 O;
energies were calculated using B3LYP/6–311þG(d,p) single
point calculations on B3LYP/6–31G(d) energy minimized structures (i.e. only the potential energy is calculated with the larger
basis set and no further relaxation of the atoms is performed).
An estimate of long-range solvation energy based on the
IEFPCM (Cancès et al., 1997; Cossi et al., 2002) was included.
Adsorption energies calculated in this manner are not expected
to give highly accurate absolute energies with respect to experiment. The assumption was made that error cancellation
would allow the relative DG-values to be used to predict which
species would be more thermodynamically favourable. In all
cases, whichever starting surface model and aqueous protonation state of orthophosphate were used, the MD-H1 was
predicted to be more thermodynamically favourable than the
BD-H0 model. For example, the pKa2 of H3PO4 is 7.2, so
both H2PO4 and HPO42– were used as aqueous species. The
surface charge of goethite is slightly positive at pH 7.5–7.9
(Parks, 1965) leading to the use of surface models with þ1 and
neutral initial charge. The DG-values calculated for the most
likely adsorption reaction (i.e. þ1 surface charge with HPO42–)
were –34 kJ mol1 for the BD-H0 surface complex and –61 kJ
mol1 for the MD-H1 configuration. The difference of –27 kJ
mol1 was expected to be significant compared to the relative
computational error, so the latter complex was more thermodynamically favoured. This configuration also gave the best fit
(slope ¼ 0.98, R2 ¼ 1.00 and RMS error ¼ 4 cm1) to the frequencies presented in Persson et al. (1996). The spectra in
Persson et al. (1996) were better resolved than those in Arai &
Sparks (2001); however, Kwon & Kubicki (2004) were able to
convolute the model frequencies to reasonably represent the
Arai & Sparks (2001) spectra based on the same calculated frequencies that matched the Persson et al. (1996) data.
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Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
Surface complexes and quantum chemical calculations 937
(a-FeOOH). Extracellular polymeric substances (EPS) were
extracted from Bacillus subtilis and Pseudomonas aeruginosa
and adsorbed onto an ATR FTIR cell coated with goethite particles. IR spectra of adsorbed EPS showed enhancement over
the aqueous spectrum for bands in the 900–1200 cm1 region
commonly associated with phosphoryl vibrations. A model
organophosphate, PO2(C5O3H9)2, was bonded to an Fe hydroxide cluster in monodentate and bridging bidentate configurations. This compound was used because it mimics the
phosphoryl groups in nucleic acids by binding two sugars to the
phosphate moiety. The bases normally linked to these sugars
were eliminated because they are located within the chain of
nucleic acids and unlikely to bind to the Fe (hydr)oxide surfaces.
The monodentate configuration gave the better correlation
to the observed frequencies (slope ¼ 1.05, intercept ¼ 48 cm1,
R2 ¼ 0.98, and RMS error ¼ 11 cm1) compared to the bidentate configuration (slope ¼ 1.06, intercept ¼ 63 cm1, R2 ¼
0.93, and RMS error ¼ 20 cm1). In addition, only the monodentate configuration predicted a vibrational frequency (near
1175 cm1) that was in the region of an observed band at 1150
cm1. This is a vibrational mode associated with P¼O double
bonds, so it is only expected in the monodentate configuration.
Estimation of adsorption energies resulted in the monodentate
configuration being more thermodynamically favourable by
–20 kJ mol1, consistent with the interpretation of the surface
complex based on the frequency correlations. This study demonstrated that phosphorylated biopolymers, either nucleic acids or
phospholipids, are a key to bacterial adhesion mechanisms onto
goethite. Judiciously chosen model systems allow bonding of
biopolymers to mineral surfaces to be modelled with relatively
small molecular clusters.
Sulphate adsorption onto Fe (hydr)oxides
Figure 3 Frequency correlations of observed and modelled modes of
orthophosphate complexes on goethite (experimental values from
Persson et al., 1996). (a) pH 4.2, (b) pH 7.9, and (c) pH 12.8.
Organophosphate and bacterial adsorption
With orthophosphate adsorption as a test case, Omoike et al.
(2004) used similar methods to interpret the molecular mechanism of bacterial exopolymer adsorption onto goethite
Paul et al. (2005) examined the effect of drying on sulphate
speciation and coordination on Fe (hydr)oxides. Previously, it
was proposed that dehydration of Fe (hydr)oxides potentially
cause a coordination and/or speciation change of adsorbed
sulphate (Hug, 1997). Measurements of dried sulphate-treated
haematite at pH 3.6 showed an IR band at c. 1200 cm1, the
intensity of which increased upon further drying (this band
was not present for hydrated samples). The same band also
appeared when haematite was in contact with aqueous sulphate acidified below pH 2, leading to speculation that the
speciation of sulphate was affected (Hug, 1997). Hence, there
was clearly a connection between the hydration state and mineral surface pH that significantly affected the speciation of
adsorbed sulphate.
Coupling MO/DFT calculations with ATR FTIR spectroscopy, Paul et al. (2005) showed that under hydrated conditions
inner-sphere sulphate adsorption occurs by either monodentate or bidentate bridging mechanisms (Figure 4), possibly
dependent upon mineral surface loading. Upon drying of the
mineral surface a fraction of sulphate protonates to form
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Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
938 J. D. Kubicki et al.
mechanisms (see Felipe et al., 2001, and references therein).
MO/DFT calculations (Paul et al., 2005; B3LYP/6–31þG(d))
were combined with experimental studies in Usher et al. (2005)
to examine the oxidation of pyrite exposed to gaseous H2O
and O2. ATR FTIR spectroscopy was used to monitor structural changes on the surface as oxidation occurred. The source
of sulphate and bisulphate O atoms was tracked by isotopically labelling the H2O and O2 with 18O, and it was found
that both reactants could contribute to (bi)sulphate formation.
MO/DFT calculations helped to interpret the ATR FTIR
spectra and identify surface complexes. Subsequent work
could then focus on modelling the oxidation of FeS2 and formation of sulphate (e.g. Rosso et al., 1999; Becker et al., 2001).
Frequencies were calculated for sulphate and bisulphate complexes bonded to Fe hydroxide clusters to mimic the oxidized
surface of pyrite, because Fe(II) is oxidized to Fe(III) simultaneously with oxidation of S(-I) to S(VI). The presence of two
complexes explains the observed frequencies: a monodentate
and a bidentate bridging bisulphate (Table 1). Examination of
Table 1 shows that one complex cannot fit the observed frequencies at either low or high H2O/O2 ratio. However, if both the
bidentate and monodentate bisulphate complexes were present, then a good match could be found for each observed frequency. The sulphate complexes resulted in predicted
frequencies that were generally too low compared to experiment, and no frequencies significantly above 1100 cm1 were
calculated for sulphate configurations (Table 1), militating
against the possibility of a sulphate surface complex.
Table 1 Observed (Usher et al., 2005) and calculated frequencies of
sulphate and bisulphate complexes bonded to an Fe(III)-(hydr)oxide
cluster. (Note that the monodentate calculated frequencies have been
updated from Usher et al. (2005) (see Paul et al., 2005) because these
particular model surface complexes were structurally improved and
the frequencies recalculated)
Observed (cm–1)
Figure 4 Inner-sphere sulphate with Fe hydroxide model surface in
(a) monodentate and (b) bidentate bridging configuration. H ¼ white,
S ¼ black, O ¼ dark grey, and Fe ¼ light grey. Graphics created
with Cerius2 (Accelrys Inc.).
High
H2O/O2
1065
bisulphate. Sulphate protonation and deprotonation behaviour is controlled by the hydration environment of the OH
group on bisulphate. These results were important because
soils naturally alternate between wet and dry conditions and
a paucity of research has been conducted on this topic, though
it may be quite significant for soil acidity.
Sulphate formed on pyrite during oxidation
In addition to modelling surface complexes and adsorption energies, computational chemistry is useful for modelling reaction
1108
1145
1165
1190
High H2 18O/O2
Calculated (cm–1)
Low
Bidentate Monodentate Bidentate Monodentate
H2O/O2 Bisulphate Bisulphate
Sulphate
Sulphate
990
1065
1107
1125
1160
1185
973
1076
901
950
992
1029
1099
906
967
1003
938
978
1005
1066
834
944
981
1067
1095
1129
1175
1188
923
1000
1065
1085
1124
1158
972
1062
928
1034
1052
1077
1170
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1100
1159
Surface complexes and quantum chemical calculations 939
Usher et al. (2005) also used H218O and 18O2 in their experiments; thus, it was possible to replace the 16O in the sulphate
group with 18O in the frequency calculations and compare
with observed results. Vibrational mode energies are sensitive
to isotopic variations (i.e. the reduced mass of the vibration),
so comparing measured and calculated 16O/18O frequency
shifts could potentially help identify the surface complexes.
Comparisons of the observed 18O-substituted vibrational frequencies with the frequencies calculated with 18O in the sulphate again favoured the bisulphate complexes over the
sulphate species (Table 1). Identification of these intermediate
species was an important step in the process of modelling
pyrite oxidation because it constrains the reaction pathway at
a point between the reactants and products. Without such
constraints along various pathways, many alternative paths
exist and modelling efforts will be wasted examining unrealistic routes of reaction.
Arsenate and arsenite adsorption onto Al and Fe
hydroxides
As(V) adsorbs in similar amounts to amorphous Al(OH)3 and
Fe(OH)3 but As(III) adsorbs more strongly to amorphous
Fe(OH)3 than to Al(OH)3. The methods employed above were
applied to the AsFe(OH)3 and AsAl(OH)3 systems to help
explain this observation. Although calculations of aqueous As
species (H3AsO3, H2AsO3, H2AsO4, and HAsO42) surrounded by eight H2O molecules reproduced observed vibrational frequencies (IR and Raman) with reasonable accuracy
(data not shown), the IR and Raman spectra of adsorbed As
species showed only one or two broad peaks between 630 and
850 cm1 (Goldberg & Johnston, 2001). Most of the surface
complexes predicted frequencies in this region, so interpretation of the surface structures based on vibrational frequencies
did not seem feasible. Computing the DG of adsorption could
be used; but, as mentioned above, this method may not be
highly accurate, with potential relative errors of more than 10 kJ mol1. Hence, it was possible that several model structures could be possible, based solely on calculated adsorption
energies. Another primary data set was necessary to reduce the
number of models that could potentially be consistent with the
experiment.
Fortunately, EXAFS studies have been carried out for As
adsorbed to Fe and Al oxy(hydr)oxides (Waychunas et al.,
1993; Fendorf et al., 1997; Manning et al., 1998; Arai et al.,
2001; Farquhar et al., 2002; Sherman & Randall, 2003). Interpretation of EXAFS data can be difficult, but the results
commonly provide coordination numbers and interatomic
distances for adsorbed species. Energy minimizations using
MO/DFT provide molecular structures as output and calculating accurate structures requires less effort than calculation of
adsorption energies or vibrational frequencies. The main concern for comparing the model calculations would be whether
the molecular clusters could accurately represent surface com-
plex interatomic distances. Based on the ability to reproduce
observed vibrational frequencies, it was assumed that the
molecular clusters would be useful to compare with EXAFS
data.
The difference in As(III) adsorption to Fe(OH)3 and Al(OH)3
was perplexing because the primary adsorption product was
thought to be the bidentate bridging configuration for both
species (Figure 5). To test this interpretation, a series of monodentate and bidentate bridging surface complexes were energyminimized (B3LYP/6–31G(d); Kubicki, 2005). In general, the
results were consistent with the previous interpretation of
Waychunas et al. (1993) and Arai et al. (2001), namely that the
bridging bidentate configurations were favoured. For example,
the observed As-O and As-Fe distances for As(III) adsorbed
onto Fe oxy(hydr)oxides were 1.78 and 3.38 Å, respectively
(Waychunas et al., 1993; Farquhar et al., 2002). The model
surface complex Fe2(OH)4(OH2)4AsO3(H2O)4 (Figure 5a)
resulted in distances of 1.76 and 1.80 Å for As-O and 3.28 Å
for As-Fe, consistent with the experiment.
One question that remained was the protonation state of
adsorbed As(III) and As(V) on the mineral surfaces. For As(III),
this question was resolved by calculating the structure of the (Al
or Fe)2(OH)4(OH2)4HAsO3 complexes. The As-OH bond
length was predicted to be 1.93 and 1.89 Å for the Al and Fe
models, respectively. This distance was significantly longer
than the observed value of 1.78 Å, so the protonated As(III)
bidentate bridging model was rejected in favour of (Al or
Fe)2(OH)4(OH2)4AsO3.
For As(V), Sherman & Randall (2003) found three As-O distances at approximately 1.71 Å and a fourth at 1.62 Å. Of the
models tested, the best fit was obtained for the Fe2(OH)4(OH2)4HAsO4 cluster where the As ¼ O distance was equal to 1.63 Å,
the As-OH bond distance was equal to 1.83 Å, and the As-O
(Fe) bond distances were equal to 1.72 Å. With H2O added
(i.e. Fe2(OH)4(OH2)4HAsO4. (H2O)4; Figure 5c), these values
changed to As¼O 1.66, As-OH 1.77, and As-O(Fe) 1.71 Å.
Protonating the AsO4 group and forming the As ¼ O appears
to be the only method for creating an As-O distance near 1.62 Å.
To model accurately As surface complexes, the protonation
state and explicit hydration were critical. The protonation state
of As(III) and As(V) species had a strong influence on the calculated bond lengths. Thus, when one is using experimental
interatomic distances to determine surface complex configurations, modelling the correct protonation state is important. Protonation and hydration are interrelated because unprotonated,
highly charged oxyanions promote Hþ transfers from the
model surface to themselves if they are not H-bonded to H2O
molecules. H-bonding directly influences the calculated oxyanion bond lengths, but to a lesser degree. When modelling
relative thermodynamic stabilities of surface complexes, the
protonation state of the oxyanion influences the calculated
energies. Larger charge differences between the negative
adsorbate and positive model surface lead to dramatic increases in calculated DG of adsorption (see Kwon & Kubicki,
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Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
940 J. D. Kubicki et al.
2004, for the effect of changing charge from 0 to þ2 for model
Fe (hydr)oxides.).
Although other configurations of As surface complexes on Fe
and Al (hydr)oxides may be possible (Waychunas et al., 2006),
the energetic analysis here focused on the bidentate bridging
configurations of As(III) and As(V). This complex is likely to
be the dominant configuration under most pH conditions.
Furthermore, comparing model DGads values was simplified
by examining similar configurations in various combinations
of As(III), As(V), model Al(OH)3 and Fe(OH)3. For As(V)
adsorption under neutral pH conditions, the following two
reactions are most likely because pKa2 of arsenious acid is 7
(i.e. [H2AsO4] ¼ [HAsO42–] at pH 7):
H2 AsO4 ðH2 OÞ8 þ M2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/M2 ðOHÞ4 ðOH2 Þ4 HAsO4ðH2 OÞ4 þ 10H2 O
and
HAsO4 2 ðH2 OÞ8 þ M2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/M2 ðOHÞ4 ðOH2 Þ4 HAsO4ðH2 OÞ4
þ ½OH ðH2 OÞ4 þ 5H2 O;
where M ¼ Al(III) or Fe(III) and the model surface has a positive
charge. The calculated DGads values for these two reactions
were –94 and –140 kJ mol1 for the first reaction on Al and Fe
(hydr)oxides, respectively, and –151 and –197 kJ mol1 for the
second reaction on Al and Fe (hydr)oxides, respectively. Thus,
As(V) adsorption was predicted to be more thermodynamically favoured onto Fe (hydr)oxide than Al (hydr)oxide, but
the DGads are both so favourable for As(V) that the adsorption sites may be saturated with respect to As(V) for both
substrates.
For As(III) adsorption, a probable reaction at pH 7 is
H3 AsO3ðH2 OÞ8 þ M2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/M2 ðOHÞ4 ðOH2 Þ4 AsO3 ðH2 OÞ4
þ 2½H3 O þ ðH2 OÞ4 :
H3AsO3 should dominate the aqueous speciation because pKa1
for arsenious acid is 9.2. The model DG adsorption was þ57
and þ14 kJ mol1 for the Al and Fe hydroxides, respectively
(Kubicki, 2005). Neither is thermodynamically favoured but
the Fe hydroxide is calculated to be significantly less positive
than the Al hydroxide reaction. The þ14 kJ mol1 value is
close to zero within our computational error.
Figure 5 (a) As(III) with H2O on Me2(OH)4(OH2)4, (b) As(V) on
Me2(OH)4(OH2)4 diprotonated without H2O, and (c) As(V) monoprotonated with H2O. H ¼ white, As ¼ black, O ¼ dark grey, and Al,
Fe ¼ light grey. Graphics created with Cerius2 (Accelrys Inc.).
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Journal compilation # 2007 British Society of Soil Science, European Journal of Soil Science, 58, 932–944
Surface complexes and quantum chemical calculations 941
Another possible reaction involves the minor species (at pH 7)
H2AsO3:
H2 AsO3 ðH2 OÞ8 þ M2 ðOHÞ5 ðOH2 Þ5þ ðE2 OÞ4
/M2 ðOHÞ4 ðOH2 Þ4 AsO3 ðH2 OÞ4 þ H3 O þ ðH2 OÞ4
þ 5H2 O:
DGads calculated for these species were þ37 and –7 kJ mol1
on Al and Fe hydroxides, respectively. The calculated DGads
value for As(III) adsorption onto Al hydroxide is positive and
slightly negative for Fe hydroxide, which is qualitatively consistent with the observation of greater As(III) adsorption to Fe
(hydr)oxide than Al (hydr)oxide (Hering et al., 1997; Dixit &
Hering, 2003). Thus, the minor H2AsO3 aqueous species will
preferentially adsorb onto Fe hydroxides and the aqueous
equilibrium will adjust by deprotonating more H3AsO3 in solution. All likely model reactions involving the protonated bidentate As(III) surface complex, M2(OH)4(OH2)4HAsO3(H2O)4,
resulted in positive calculated DGads values. Consequently, the
Fe2(OH)4(OH2)4AsO3(H2O)4 species (Figure 5a) appeared to
be the most likely on Fe hydroxides, based on Gibbs free
energy calculations. This conclusion was the same as that
based on comparing interatomic distances from EXAFS with
the molecular models. The fact that both approaches point
toward the same surface complex helps validate this approach
and strengthen the conclusions drawn from it.
Comparison of model adsorption energies
Although calculating absolute reaction Gibbs free energies for
mineral–water interface reactions is challenging, it can be
instructive to compare the relative model DGads for this series
of oxyanions (see Radu et al., 2005 for examples). Because
these calculations can be conducted self-consistently, the relative adsorption energies provide insight into the thermodynamic favourability of adsorption in multicomponent systems.
This is especially true for the species of interest here (carbonate, phosphate, sulphate, arsenate and arsenite) because these
compounds may adsorb at similar sites on Fe and Al (hydr)
oxide surfaces.
The aqueous species HCO3, H2PO4, HPO4, SO42,
H2AsO4, HAsO4, H3AsO3 and H2AsO3 were chosen
because these should be present in finite quantities at pH 7
according to their pKa values (Faure, 1998). Other species
could be included to examine model predictions at other pH
values, but, for the sake of simplicity, only these species will be
discussed here. The product surface complexes were selected
based on comparisons to experimental data as discussed above.
To further simplify the comparison, model surface sites with
a þ1 charge were included as potential reactants. Restricting
the analysis to the þ1 model surface helped limit the role of
electrostatics in the calculated adsorption energies. Aqueous
species of identical charge could not be used in each case, however, because we were constrained by the species that actually
exist in solution. Hence, electrostatics still play a role in the calculated adsorption energies, but the nature of our calculations
allows for implicit inclusion of this factor in our model results.
Neutral adsorption sites can also be important, but the adsorption energies were consistently larger for the þ1 model surface,
so these sites should dominate adsorption in real systems when
the concentrations of potential adsorbates are small.
The following DGads were modelled at the B3LYP/
6–311þG(d,p)//B3LYP/6–31G(d) level of theory with the
Gibbs free energy from the IEFPCM solvation model (Cancès
et al., 1997) corrected by the gas-phase thermal correction to
the Gibbs free energy with the B3LYP/6–31G(d) method:
HCO3 ðH2 OÞ6 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 CO3ðH2 OÞ6 þ 1:2½ðH2 OÞ5 ¼ 51 kJ mol 1
H2 PO4 ðH2 OÞ8 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 H2 PO4þ ðH2 OÞ4
þ ½OH ðH2 OÞ4 þ 5H2 O ¼ þ 75 kJ mol 1
H2 PO4 ðH2 OÞ8 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 HPO4þ ðH2 OÞ4 þ 10H2 O
¼ 128 kJ mol 1
H2 PO4 ðH2 OÞ8 þ ½Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4 /Fe2 ðOHÞ4 ðOH2 Þ5 HPO4ðH2 OÞ6 þ 1:4½ðH2 OÞ5 ¼ 88 kJ mol 1
H2 PO24 ðH2 OÞ8 þ ½Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4 /Fe2 ðOHÞ4 ðOH2 Þ5 HPO4ðH2 OÞ6
þ ½OH ðH2 OÞ4 þ 0:4½ðH2 OÞ5 ¼ 76 kJ mol 1
SO24 ðH2 OÞ9 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 SO4ðH2 OÞ4 þ ½OH ðH2 OÞ4 þ 1:2½ðH2 OÞ5 ¼ 66 kJ mol 1
H2 AsO4 ðH2 OÞ8 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 HAsO4ðH2 OÞ4 þ 10H2 O
¼ 140 kJ mol 1
HAsO24 ðH2 OÞ8 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 HAsO4ðH2 OÞ4
þ ½OH ðH2 OÞ4 þ 5H2 O ¼ 197 kJ mol 1
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942 J. D. Kubicki et al.
H3 AsO3ðH2 OÞ8 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 AsO3 ðH2 OÞ4
þ 2½H3 O þ ðH2 OÞ4 ¼ þ 14 kJ mol 1
H2 AsO3 ðH2 OÞ8 þ Fe2 ðOHÞ5 ðOH2 Þ5þ ðH2 OÞ4
/Fe2 ðOHÞ4 ðOH2 Þ4 AsO3 ðH2 OÞ4
þ H3 O þ ðH2 OÞ4 þ 5H2 O ¼ 7 kJ mol 1
From the above model adsorption energies, a few observations
can be made. First, the effect of charge on the solute molecule on
the calculated results is clear. Comparing the energies of the
H2AsO4 and HAsO42– reactions shows an increase from –140
to –197 kJ mol1 in favourability. Thus, using the appropriately charged species for comparison with experiment is critical in determining the most likely reactions. Of course, in
a real system, as pH increases to favour HAsO42– over
H2AsO4, the likelihood of interacting with positively charged
surface sites such as Fe2(OH)5(OH2)5þ also decreases.
A comparison of the model DGads of carbonate, arsenate and
phosphate shows that DGads of arsenate > phosphate > carbonate. This result is consistent with the observation of Radu
et al. (2005), who found that greater aqueous carbonate concentrations did not significantly displace adsorbed arsenate
and that arsenate adsorbs more strongly than phosphate
(Radu et al., 2005). We note that the calculated phosphate
DGads is not thermodynamically favourable when the diprotonated, bidentate species Fe2(OH)4(OH2)4H2PO4þ(H2O)4 is
the product. This is consistent with our previous calculations
that showed the singly protonated, monodentate species as the
stable surface complex near circumneutral pH based on comparison to IR frequencies and calculated adsorption energies
(Kwon & Kubicki, 2004). The predicted thermodynamic
favourability of sulphate adsorption was comparable with
phosphate, and hence may compete effectively with similar
adsorption sites. Experimental testing of this prediction would
be useful in evaluating our computational approach.
Conclusions
Computational chemistry is a useful tool for studying surface
reactions when used in combination with a variety of experimental techniques. Although system size and level of theory can limit
the accuracy of these model calculations, results can be determined reliably enough to distinguish among various hypothesized structures. A good strategy is to use the flexibility of the
MO/DFT calculations to predict a variety of experimentally
observable properties, such as interatomic distances, vibrational
frequencies and reaction free energies. Discovering one model
that fits all the data best provides confidence in the molecular
model derived from this effort. Interaction between experimentalists and modellers creates a feedback that improves the
thought process from both aspects of a given research project.
Recently, there has been a growing number of studies involving
experimental IR work in conjunction with MO/DFT computations. However, systematic studies are required to answer fundamental questions with respect to surface complexation, for
example:
1 How do vibrational frequencies change from solution to
mineral surface complexes (e.g. new frequency emergence or
shifting, etc.)?
2 How do chemical bonds between anions and mineral surface
Fe atoms affect the system energy and oxyanion geometries?
3 Can we generalize the complex trends in observed vibrational frequencies and bonding geometries?
Increasing computational speed will continue to make it easier
to produce high-quality computations on realistic systems in the
future.
Acknowledgements
This research was funded by the NSF grant CHE-0221934
‘Stony Brook-BNL collaboration to establish a Center for
Environmental Molecular Sciences (CEMS)’. Computation was
supported in part by the Materials Simulation Center, a PennState MRSEC and MRI facility, and the Center for Environmental Kinetics Analysis (CEKA), a NSF/DOE Environmental
Molecular Sciences Institute.
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# 2007 The Authors
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